Summary: J. Parallel Distrib. Comput. 64 (2004) 974­996
Fast optimal load balancing algorithms for 1D partitioning$
Ali Pinara,1
and Cevdet Aykanatb,
*
a
Computational Research Division, Lawrence Berkeley National Laboratory, USA
b
Department of Computer Engineering, Bilkent University, Ankara 06533, Turkey
Received 30 March 2000; revised 5 May 2004
Abstract
The one-dimensional decomposition of nonuniform workload arrays with optimal load balancing is investigated. The problem
has been studied in the literature as the ``chains-on-chains partitioning'' problem. Despite the rich literature on exact algorithms,
heuristics are still used in parallel computing community with the ``hope'' of good decompositions and the ``myth'' of exact
algorithms being hard to implement and not runtime efficient. We show that exact algorithms yield significant improvements in load
balance over heuristics with negligible overhead. Detailed pseudocodes of the proposed algorithms are provided for reproducibility.
We start with a literature review and propose improvements and efficient implementation tips for these algorithms. We also
introduce novel algorithms that are asymptotically and runtime efficient. Our experiments on sparse matrix and direct volume
rendering datasets verify that balance can be significantly improved by using exact algorithms. The proposed exact algorithms are
100 times faster than a single sparse-matrix vector multiplication for 64-way decompositions on the average. We conclude that exact